Luis buys a movie club card for $15 and then pays $7 for each movie ticket he purchases. If his total spend is $64, how many movie tickets does Luis buy?
A linear cost model fits a purchase with a one-time fee and a price per item. Multiply the item price by the number of items, add the fee once, and set the sum equal to the total. Then use a one-unknown regression in Desmos to find the count. The fee does not repeat with each item.
Hints
- Hint 1
Let count the tickets. A rate is a price per ticket, so multiply the ticket price by to get the ticket spending. Which charge stays fixed no matter how many tickets Luis buys?
- Hint 2
A total-cost equation adds the charges in dollars. Add the one-time fee to the cost of the tickets, then set that sum equal to the amount Luis spent. What equation does that give you?
Step-by-step
Model the cost, then solve in Desmos
Step 1Write the total-cost equation
Let be the number of tickets. The $15 card is bought once, while $7 for each ticket makes the ticket cost . Those costs add to the total spending of $64, so . Multiplying the card price by would charge Luis for a new card with every ticket.
- Step 2
Find and interpret the ticket count
Type in Desmos. Replace with because Desmos graphs but can find ; the tells its regression to make both sides equal. Under PARAMETERS, Desmos shows . Since the unknown counts tickets, Luis buys 7 movie tickets. Choice C.